USE OF THE MANN-WHITNEY U TEST


The Mann-Whitney U can be applied when you have two independent, randomly selected groups of unequal sizes. It tests whether two independently drawn samples have been drawn from the same population. To do the comparison, the experimenter must rank the data. Once that is done, then the question is: Do the scores from one sample significantly differ from those of the other sample, so that we can conclude each sample represents a different population, or is the difference due to the luck of the draw? In the latter case we would conclude that, though the samples may differ , they represent the same population. The decision is made on the critical value as identified in a special table of values for this test. The requirements for the Mann-Whitney U are as follows :

  1. Ordinal data

  2. Two groups

  3. Independently drawn samples

  4. Data in ranks

  5. Simple random samples

  6. Sample size can be different for the two groups.

When the n 2 is between 9 and 20 then the formulas for the test are:

  1. Mann-Whitney U

  2. Mann-Whitney U

    U 2 = n 1 n 2 - U 1

The reason that two formulas are necessary is that we need to find the smaller U of the two. Since we are dealing with two populations, usually of different sizes, it stands to reason the two formulas will give different values of U. We perform both tests for U, and whichever happens to be smaller is used as our U value. Do not worry if you do not understand these formulas now; just look at them. The symbols we use for computing and understanding the formulas are n 1 = size of smaller group , n 2 = size of larger group, N = total number in both groups (n 1 + n 2 ), & pound ; R 1 = sum of the ranks in group one, R 2 = sum of the ranks in group two.

When n 2 is larger than 20, then the Mann-Whitney U test is:

Obviously, when n 2 is larger than 20, you have to carry out some further calculations. In this case you use your value of U to compute the value of z given by the formula. The sampling distribution for z is approaching the normal distribution, and as a consequence, the table values for the z are appropriate. That means that you reject the null hypothesis if the probability for z is equal to or less than the predetermined level of significance. The one-tailed probabilities are given in the z table; for two-tailed probabilities double the table values.




Six Sigma and Beyond. Statistics and Probability
Six Sigma and Beyond: Statistics and Probability, Volume III
ISBN: 1574443127
EAN: 2147483647
Year: 2003
Pages: 252

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